Solve the triangle



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Solving the triangle

From the perspective of knowledge structure, Pythagorean theorem reveals the quantitative relationship between the three sides of a right triangle, provides an important theoretical basis for subsequent learning to solve a right triangle, and is widely used in real life. This lesson is for students to learn on the basis of mastering the relevant properties of the right triangle. Through the story of the pattern on a stamp issued by Greece in 1955, the Pythagorean theorem is introduced, and then the quantitative relationship of the three sides of the right triangle is explored and applied to solve problems. Learning this section well will not only lay a good foundation for the inverse theorem of Pythagorean theorem in the next section, but also lay a foundation for learning to solve right triangle in the future. At the same time, it will be of great use in real life. Pythagorean theorem is a very important property of right triangle and a very important theorem in geometry. It reveals the quantitative relationship among the three sides of right triangle and closely links the number and shape. It has rich historical background and occupies an important position in theory. The trilateral relationship of a right triangle in the eighth grade of the Chinese Normal University Edition is a section of content after students learn the square root of numbers and the multiplication and division of integers. It is learned by students on the basis of having mastered the relevant properties of right triangles. It reveals the quantitative relationship between the three sides of a right triangle and paves the way for solving right triangles later. It is also the most important theorem in geometry, which closely links shapes and numbers, It plays an important role in the development of mathematics. Pythagorean theorem is learned by students on the basis that they have mastered the relevant properties of right triangle. It is a very important property of right triangle and one of the most important theorems in geometry. It reveals the quantitative relationship between the three sides of a triangle. It can solve the calculation problems in right triangle, is one of the main bases for solving right triangle, and is very useful in real life. When compiling textbooks, attention should be paid to cultivating students' hands-on operation ability and problem analysis ability. Through practical analysis, puzzles and other activities, students can get a more intuitive impression; Through contact and comparison, we can understand the Pythagorean theorem so as to correctly apply it. 17. This question mainly examines the comprehensive application of the sine theorem, the tangent formula of the sum of two angles, the cosine theorem, and the area formula of triangles in solving triangles, and examines the transformation idea, which belongs to the basic question. Question 17. This question mainly examines the comprehensive application of the sine theorem, the tangent formula of the sum of two angles, the cosine theorem, and the area formula of triangles in solving triangles, and examines the transformation idea. It belongs to the basic question. In particular, for some functions, it is a must to solve triangles. It is crucial to carry out more accurate induction! The following is the necessary database for Mr. Hong's college entrance examination. Full Score training for typical big questions in high school mathematics: strategies for solving triangles and accurate induction of question types! Data No.: 093 Pythagorean theorem is the content of the first lesson in the first section of Chapter 18 of Grade 8 Mathematics in the new curriculum standard of the people's Education Edition. Pythagorean theorem is learned by students on the basis of having mastered the relevant properties of right triangle. It is one of several important theorems in middle school mathematics. It reveals the quantitative relationship between the three sides of a right triangle. It is one of the main bases for solving a right triangle and is very useful in real life. The discovery, verification and application of Pythagorean theorem contains rich cultural value. It occupies an important position in theory. It is very important to learn this section well. Most of the problem-solving skills involved in the topic have been practiced many times, such as the number sequence problem, the conic curve, the solution of triangles and the identity transformation of trigonometric functions in the big question. These three big questions have a total of more than 30 points. For students who learn better, it is equivalent to sending points. They don't need to think much. The ideas are ready-made, and the scores should be basically obtained. The big problem of solid geometry is also very familiar, and it is not difficult to get points. [basis for postponement] the investigation of solving triangles in the national volume is generally geometric and pure algebraic rotation. The new volume 1 in 2022 investigates and understands pure algebraic analysis in triangles, so the author carefully selects a problem of solving triangles involving geometric properties to comprehensively investigate and understand the most basic knowledge points involved in triangles: the centerline and the bisector of angles. Among them, the problem of solving triangles related to the bisector of angles has not been investigated in the national volume for many years, and there are few simulation problems related to it at ordinary times, which belongs to key and unpopular knowledge and needs to be paid attention to. The difficulty of this question is moderate, and students with a good foundation (100 +) should all get full marks. The content reviewed in this lesson is to solve the problem of the maximum range of triangles, which is a comprehensive application of trigonometric functions, trigonometric identity transformation, sine theorem and cosine theorem. Solving triangles is a powerful means to deal with quantitative calculation of planar geometry, and also lays a good foundation for calculation in spatial solid geometry. Solving triangles also reflects the instrumental role of vectors, and is also a continuation of vector learning. At the same time, the plane can be transformed into geometric coordinates, and the triangle can be studied analytically. It is precisely because of the intuitive shape of triangles, as well as the operation of number such as side length, angle and coordinate, that triangles become a good carrier for examining all kinds of comprehensive knowledge and thinking about the combination of number and shape. The introduction of the maximum range in the solution of triangles is also ingeniously integrated with the idea of functions and equations. Studying the maximum range of trigonometric function can improve students' logical thinking ability and computing and solving ability. Summary: Changning 25 focuses on the ability of students to solve triangles. The flexible use of parallel type (a or x) is a popular test point in the mid-term exam in the past three years. Please don't ignore it. The problem of trigonometric functions and solving triangles is to connect functions with triangles. Unlike elementary functions and derivative functions, this section is relatively simple. As long as you master the core formulas and angle changes, and skillfully use them in brushing questions, you can flexibly solve problems! But the difficulty is that many students do not thoroughly analyze the question type! I have no idea how to solve the problem! The main contents of this chapter include: acute angle trigonometric functions (sine, cosine and tangent), and solving right triangle. Acute angle trigonometric function is the trigonometric function when the independent variable is acute angle, that is, the trigonometric function after narrowing the definition domain. Solving right triangles is widely used in practice. Acute angle trigonometric function provides an effective tool for solving right triangles. The knowledge of similar triangles is the direct basis for learning acute angle trigonometric functions. Pythagorean theorem and other contents are also mathematical conclusions often used in solving right triangle. Therefore, this chapter is closely related to Pythagorean theorem and similarity in Chapter 18. This idea has some truth, but it does not completely conform to the objective facts. Because the three body problem can't give a general solution, but it has an accurate solution in special cases (for example, the three stars are distributed in a triangle and rotate around the center of the triangle).

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